Fractions+Theoretical+Background

Fractions Theoretical Background (Knol, n.d.)

**Big Ideas (I Stock Photo,n.d.) **

//According to Van De Walle, Karp and Bay-Williams (2010), there are five big ideas that need to be considered when teaching fractions// **Fractions history (Basic-mathematics.com, n.d.) **
 * Fractions must be experienced via different constructs and must include parts of a whole, ratios and division.
 * Length (1/3 of an inch), Area (1/2 of a garden) and Set or Quantity (1/4 of the class) are the three models for fractions.
 * Understanding the meaning of fractions, especially numerators and denominators are developed by partitioning and iterating.
 * Estimating with fractions using a variety of experiences is important.
 * The understanding of equivalent fractions is imperative. The same amount can be demonstrated by two equivalent fractions by using different sized fractional parts.

** Queensland Syllabus Approach to Fractions ** // Students are first introduced to fractions during the early years, by the end of the Year 3 juncture (Essential Learnings, 2007). // ** Key Understandings of Fractions **
 * Robbins and Hauge (1999) suggest it took a long time to develop a way to write fractions symbolically.
 * The Chinese used concepts relating to fractions in commerce in 1100BC (Robbins & Hauge, 1999).
 * Babylonian's used concepts relating to fractions for measurement and trade (Robbins & Hauge, 1999).
 * Ancient Romans used concepts relating to fractions to divide up estates (Robbins & Hauge, 1999).
 * According to Robbins & Hauge (1999), previous symbolic history of fractions is very different to the current fraction notation. For example: Greeks used a measuring vessel cut in half to represent 1/2. A cross with four arms was an early Egyptian symbol used to represent 1/4.
 * Babylonians used a denominator of 60, during ancient times and Romans used a denominator of 12 only (Robbins & Hauge, 1999).
 * Robbins and Hauge (1999) highlighted that numerators greater than one rose in Babylon
 * The bar between the numerator and denominator possibly arose by the Arabs (Robbins & Hauge, 1999).
 * Geoffrey Chaucer first used the word 'fraction' in the 1300's (Robbins & Hauge, 1999).
 * Prior to the 1300's, fractions were referred to as 'broken numbers', according to Robbins and Hauge (1999).
 * The number organiser within the Essential Learnings syllabus (2007) addresses fractions and specific outcomes in regards to fractions//.//
 * "Simple Fractions, including half and quarter, and mixed numbers can be represented in different ways" (Queensland Studies Authority, 2007, p.2).
 * According to Jamieson-Proctor (2010) fractions can be defined as an equal part of a whole and less than one.
 * There are four types of fractions, which include; common, decimal, percent and ratio (Jamieson-Proctor, 2010).
 * Jamieson-Proctor (2010) suggests that fractions should be taught very carefully, using common fractions to begin with.
 * Mental pictures of common fractions must be able to be visualised (Jamieson-Proctor, 2010).
 * Jamieson-Proctor (2010) proposes that educators need to relate parts to the whole to develop the part-whole relationship.
 * Jamieson-Proctor (2010) details the 3 models that are used to develop the fractions concept these include; Length, Area and Set models.

Basic-mathematics.com. (n.d.). //History of Fractions// [image]. Retrieved September 18, 2010 from [] I Stock Photo. (n.d.). //Lightbulb moment as inspiration strikes!// [image]. Retrieved September 18, 2010 from [] Jamieson-Proctor, R. (2010). //EDX 1280 Foundations of Numeracy Lecture 8 Week 8.// Retrieved from []

Knol. (n.d.). //Learning to appreciate fractions// [image]. Retrieved September 17, 2010 from []# Queensland Studies Authority. (2007). //Mathematics Essential Learnings by the end of Year 3.// Retrieved September 18, 2010 from [] Robbins, P., & Hauge, S. (1999). //Word Problems with Fractions.// Portland, Maine: J. Weston Walch Publisher. Van De Walle, J., Karp, K., & Bay-Williams, J. (2010). //Elementary and Middle School Mathematics Teaching Developmentally// (7th ed.). USA: Pearson Education Inc.